The Gibbs paradox

Quanmin Guo

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arXiv · 2106.05868

The Gibbs paradox

Quanmin Guo

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Abstract

Molecular collision within an ideal gas originates from an intrinsic short-range repulsive interaction. The collision reduces the average accessible physical space for a single molecule and this has a direct consequence on the entropy of the gas. The accessibility of a molecule to a spatial coordinate (x, y, z) inside the system depends on the local molecular density. By considering mechanical equilibrium between a system and a reservoir, the probability of the system in state i with volume vi is shown to be proportional to exp(-vi/v0) where v0 is the average volume per molecule. Incorporating this factor into the single particle partition function automatically leads to an N-particle entropy that is extensive without applying the N! correction factor. The exp(-vi/v0) factor plays a similar role in describing the volume distribution as the Boltzmann factor which governs the energy distribution.

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Quanmin Guo. 2021-06-06. The Gibbs paradox. https://arxiv.org/abs/2106.05868

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